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Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0...

Consider: `L_1:2x+3y+p-3=0` `L_2:2x+3y+p+3=0` where `p` is a real number and `C : x^2+y^2+6x-10 y+30=0` Statement 1 : If line `L_1` is a chord of circle `C ,` then line `L_2` is not always a diameter of circle `Cdot` Statement 2 : If line `L_1` is a a diameter of circle `C ,` then line `L_2` is not a chord of circle `Cdot` Both the statement are True and Statement 2 is the correct explanation of Statement 1. Both the statement are True but Statement 2 is not the correct explanation of Statement 1. Statement 1 is True and Statement 2 is False. Statement 1 is False and Statement 2 is True.

A

Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I

B

Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I

C

Statement I is true, Statement II is false

D

Statement I is false, Statement II is true

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The correct Answer is:
C
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Consider, L_(1) : 2x + 3y + p – 3 = 0 , L_(2) : 2x + 3y + p + 3 = 0 , where p is a real number, and C : x^(2)+y^(2)+6x–10y+30=0 Statement-I : If line L_(1) is a chord of circle C, then line L_(2) is not always a diameter of circle C. and Statement-II : If line L_(1) is a diameter of circle C, then line L_(2) is not a chord of circle C.

The equation of the diameter of the circle x^2 + y^2 + 4x + 4y-11=0 , which bisects the chord cut off by the circle on the line 2x-3y-3=0 is 3x+2y+10=0 . Statement 2 : The diameter of a circle is a chord of the circle of maximum length. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not a correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Condider the lines L_(1):3x+4y=k-12,L_(2):3x+4y=sqrt2k and the ellipse C : (x^(2))/(16)+(y^(2))/(9)=1 where k is any real number Statement-1: If line L_(1) is a diameter of ellipse C, then line L_(2) is not a tangent to the ellipse C. Statement-2: If L_(2) is a diameter of ellipse C, L_(1) is the chord joining the negative end points of the major and minor axes of C.

Statement-1: The lines y=mx+1-m for all values of m is a normal to the circle x^(2)+y^(2)-2x-2y=0 . Statement-2: The line L passes through the centre of the circle.

y=2x is a chord of the circle x^(2)+y^(2)-10x=0, then the equation of a circle with this chord as diameter is

Consider circles C_1 : x^2 +y^2 + 2x-2y + p = 0, C_2 : x^2+y^2-2x+2y-p=0 and C_3 : x^2+y^2=p^2 Statement I: If the circle C_3 intersects C_1, orthogonally then C_2 does not represent a circle Statement II: If the circle C_3, intersects C_2 orthogonally then C_2 and C_3 have equal radii. Then which of the following statements is true ?

ARIHANT MATHS-CIRCLE -Exercise (Questions Asked In Previous 13 Years Exam)
  1. A circle is given by x^2 + (y-1) ^2 = 1, another circle C touches it e...

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  2. If the circles x^2+y^2+2a x+c y+a=0 and points Pa n dQ , then find the...

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  3. A circle touches the x-axis and also touches the circle with center (...

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  4. If a circle passes through the point (a, b) and cuts the circlex x^2+y...

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  5. Let ABCD be a square of side length 2 units. C2 is the circle through ...

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  6. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  7. ABCD is a square of side length 2 units. C(1) is the circle touching ...

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  8. If the lines 3x-4y-7 = 0 and 2x-3y-5=0 are two diameters of a circle o...

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  9. Let C be the circle with centre (0, 0) and radius 3 units. The equatio...

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  10. Tangents are drawn from the point (17, 7) to the circle x^2+y^2=169, S...

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  11. Consider a family of circles which are passing through the point (-...

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  12. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  13. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  14. A circle C of radius 1 is inscribed in an equilateral triangle PQR. Th...

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  15. Consider: L1:2x+3y+p-3=0 L2:2x+3y+p+3=0 where p is a real number and...

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  16. The point diametrically opposite to the point P(1, 0) on the circle x^...

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